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Consider the function \(z=\sqrt{2x^2+2y^2}\). What is the direction of steepest ascent at the point \( (1,1) \)?
Please select all the correct statements about the gradient.
Given the following function The gradient of f at (x,y) = (1,1) is
Tasks: Let's continue taking partial derivatives. Go to Example 11.3 and work through yourself how the three derivatives (with respect to ๐ฅ , ๐ฆ , and ๐ง ) were computed. At the end of Example 11.3 we are also introduced to the definition of the gradient of a function. If ๐ is a function of ๐ variables and all the partial derivatives exist, then the gradient of ๐ is defined to be โ ๐ ( ๐ฅ ) = ( โ ๐ โ ๐ฅ 1 ( ๐ฅ ) , โ ๐ โ ๐ฅ 2 ( ๐ฅ ) , โฆ , โ ๐ โ ๐ฅ ๐ ( ๐ฅ ) ) . This video goes over the definition and some facts on notation: Question: Which of the following functions have gradient โ ๐ = ( ๐ฆ ๐ ๐ฅ ๐ฆ + ๐ฆ , ๐ฅ ๐ ๐ฅ ๐ฆ + ๐ฅ ) ?
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